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1Center for Systems Engineering and Applied Mechanics, Université Catholique de Louvain, Louvain-la-Neuve; and 2Laboratory of Neurophysiology, Université Catholique de Louvain, Brussels, Belgium
Submitted 25 March 2005; accepted in final form 31 August 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Several studies investigated the programming of saccades to moving targets in one dimension (1D; horizontal). It was first thought that catch-up saccades to step-ramp stimuli were not predictive (Heywood and Churcher 1981
). However, in subsequent studies, it was shown that target motion was indeed taken into account (Gellman and Carl 1991; Keller and Johnsen 1990; Kim et al. 1997; Ron et al. 1989). These previous studies did not agree on the exact nature of the predictive component. In fact, two different signals could play this role: the target velocity and the retinal slip. Recently, de Brouwer et al. quantitatively studied catch-up saccades in the cats (de Brouwer et al. 2001) and in humans (de Brouwer et al. 2002). They showed first that retinal slip was better correlated with catch-up saccade amplitude than the target velocity. More precisely, both position error and retinal slip were used to calculate catch-up saccade amplitude and a model was proposed for the catch-up saccade programming. These results are in agreement with the effects of retinal slip on saccade amplitude found by Guan et al. (2005) for monkeys.
Visual tracking of moving targets in two dimensions has been studied by Engel et al. (1999) and de'Sperati and Viviani (1997). de'Sperati and Viviani (1997) studied the smooth pursuit response to elliptic target motion, whereas Engel et al. (1999) analyzed the smooth and saccadic responses to a sudden change in the direction of target motion (constant velocity). In their report, Engel et al. (1999) showed that the direction of the first saccade after the change in target trajectory was influenced by target velocity. This is consistent with the quantitative analysis of horizontal catch-up saccades (de Brouwer et al. 2002), showing that saccades predict future target position. However, until now, there has been no systematic investigation of catch-up saccades characteristics in 2D. Saccades toward stationary targets have been well documented. A significant proportion are not straight and present some curvature. Viviani et al. (1977) first reported a faster onset of the horizontal component over the vertical one in oblique saccades, which leads to systematic curvatures. This was confirmed and quantified later (Smit and Van Gisbergen 1990). Saccadic curvature was systematic and direction-dependent: saccades present continuous patterns less curved for cardinal directions and with maximal curvatures for oblique saccades. A stretching of the shortest component has also been reported in cats (Evinger et al. 1981; Guitton and Mandl 1980) and in monkeys and humans (Becker and Jürgens 1990; Smit et al. 1990; van Gisbergen et al. 1985).
In this study, we combined random and sudden position and velocity steps of the target and analyzed the characteristics of 2D catch-up saccades. We quantified the influence of position and velocity errors on the amplitude and the curvature of catch-up saccades. For the first time, this bidimensional paradigm allowed the demonstration of an asynchrony between the estimation of position and velocity errors that deeply influenced the characteristics of catch-up saccades. Using this bidimensional paradigm in electrophysiological studies should be an excellent tool to shed light on the interaction between the saccadic and smooth pursuit systems.
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METHODS |
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Experimental set-up
Subjects were seated in darkness and faced a tangent screen 1 m away, which spanned about ±45° of their visual field. Their head was restrained by a chin-rest. The target was a red laser spot of 0.2°, controlled by mirror-galvanometers. It was back-projected onto the screen and moved in 2D. The 2D movements of one eye were recorded with the scleral search coil technique (Collewijn et al. 1975; Robinson 1963).
Experimental paradigm
Sessions of maximum one-half of an hour were divided in blocks of trials. The first two blocks were made of 40 control trials to stationary targets, followed by blocks of 30 test trials (the total number of blocks was 
47 for each subject). For both trial conditions, subjects were instructed to fixate the target and follow its motion as accurately as possible throughout the trial. Control trials were composed of an initial fixation period at the center of the screen followed by a step of the target to the periphery. Both periods of initial and peripheral fixations varied randomly between 700 and 1,300 ms. The target step varied randomly between –20 and +20 ° horizontally and vertically. Test trials consisted of double-step-ramp stimuli. They started with a constant fixation period (800 ms) at an eccentric position randomly chosen among eight possible fixation targets located on a 15 ° circle (see example in Fig. 1). After this initial fixation period, the target stepped away in the periphery and smoothly moved toward the center of the screen (Rashbass step-ramp stimulus). The amplitude of the step was adjusted in such a way that the target crossed the initial fixation point after 200 ms (Rashbass 1961), and the velocity of the ramp (TV1) varied randomly and continuously between 10 and 20°/s. The duration of the ramp varied between 600 and 1,100 ms. The first ramp was followed by a second step-ramp of the target. The position step (PS) and the velocity step (VS) of the target varied randomly in both horizontal and vertical directions between –10 and 10 ° and –40 and 40°/s, respectively. In this study, we were particularly interested in the saccadic response to the second ramp (range of change in direction: 0–360°). We wanted to study the role of retinal information in this process, and consequently, we reduced the influence of cognitive factors by randomizing in each trial the starting point, the orientation, and the speed of the second ramp. The duration of the second ramp varied between 500 and 700 ms. Trials ended with a fixation period of 500 ms at the final position of the second ramp.
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Horizontal and vertical eye and target position were sampled at 500 Hz. They were stored on the hard disc of a PC for off-line analysis. MATLAB (Mathworks) was used to implement digital filtering, velocity, and acceleration algorithms. Position signals were low-pass filtered by a zero-phase digital filter (cut-off frequency: 50 Hz). Velocity and acceleration were derived from position signals using a central difference algorithm.
Saccades were detected with a vectorial acceleration threshold of 750°/s2. In the double-step-ramp protocol, we analyzed the first catch-up saccade triggered after the second target step. A total of 3,291 control saccades and 16,242 catch-up saccades were analyzed. The latency of catch-up saccades was measured with respect to the second target step. Only saccades with a minimum latency of 100 ms were considered for further analysis (n = 14,578). Indeed, most catch-up saccades with shorter latency were oriented toward the first target ramp, because they were based on sensory signals measured before the second target step (de Brouwer et al. 2002). Linear addition of saccadic and smooth component was shown for horizontal saccades (de Brouwer et al. 2002). When smooth and saccadic components are in the same direction, catch-up saccades are larger than control saccades of identical duration. Thus a correction is needed to take into account the influence of smooth pursuit. In all analyses, the smooth component was estimated using the saccade duration (D) and the mean smooth pursuit eye velocity during the saccade (V, computed as the average of the velocity before and after the saccade). It was then removed from the measured amplitude (S) to focus on the saccadic part (corrected amplitude = S*) of the catch-up saccade: S* = S –(D x V). Defining the ideal vectorial saccadic amplitude as the vectorial length of a saccade that brings the eye on the target, the saccadic gain which represents the saccadic accuracy was defined as: 1 – final vectorial error/ideal vectorial saccadic amplitude. Its value is 1 when the eye is on the target at the end of the saccade. Two major sensory parameters were extracted: position error (PE) and retinal slip (RS), both measured 100 ms before saccade onset (PE100 and RS100). We considered their horizontal and vertical components (PE100X and PE100Y, RS100X and RS100Y), their vectorial length 
, and their orientation [counterclockwise in the range (0, 360°), an orientation of 0 ° indicating an horizontal vector directed to the right]. We defined the initial and final saccade orientations (Oinit and Ofin) as the orientation of the first and last 20 ms of the saccadic movement, respectively. We also defined a measure of curvature as the difference between these orientations (curvature = Oinit – Ofin). This curvature was positive for a saccade curved in a clockwise direction and negative for a saccade curved in a counterclockwise direction.
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RESULTS |
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A first trial with a typical straight saccade is represented in Fig. 2. In most trials, the eye movement started with a purely smooth eye movement in response to the Rashbass step-ramp, and the eye velocity approximated target velocity before the end of the first ramp. A catch-up saccade was triggered after the second step in position and velocity of the target, with a latency of 
180 ms. Isochronic lines connect the eye and target position at the same instant in time and thus represent PE. The orientation of PE100 and RS100 is also represented. This shows that the saccade compensated for PE100, but also took into account RS100. Indeed, the saccade should have been parallel to the PE solid arrow if only PE100 had been compensated for. Instead, horizontal and vertical saccadic components were combined to produce an accurate straight catch-up saccade, directed toward the extrapolated position of the target. Thus as the future position of the target was accurately predicted, an evaluation of RS has been taken into account in the saccade programming. Figure 3 shows a second category of trials. The catch-up saccade was accurate but abruptly changed direction in midflight. More precisely, a change in direction was observed in the horizontal component. Two different parts could be distinguished in the saccadic movement (Fig. 3, open arrow). The first part was oriented toward the target position at the moment of saccade onset, thus compensating for PE principally and weakly for RS. However, the isochronic lines show that the error at the end of this first saccadic part was still significant. The direction of the second part of the saccade changed to better catch the moving target. This second part seemed to compensate for RS principally. Such saccades presented nonregular velocity profiles, with a double peak. The minimum vectorial velocity between the two peaks was very high and larger than the mean smooth pursuit eye velocity for 89% of the saccades. Double-peaked saccades were observed in all subjects. Their occurrence did not depend on the duration of the experimental sessions or subjects fatigue. Therefore we divided the data in two categories of catch-up saccades, that were named single-peaked saccades (single peak vectorial velocity profile, n = 12,853) and double-peaked saccades (n = 1,556), respectively. We analyzed and compared these two categories. Moreover, as shown in Fig. 3, the two parts of double-peaked saccades seem to compensate for PE and RS, respectively. It was thus necessary to analyze them separately: the first part was defined from the beginning of the saccade until the minimum of the vectorial velocity profile, and the second part was defined from this minimum until saccade end.
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For single-peaked saccades, the relationship between corrected vectorial amplitude and saccade duration was characterized by the main sequence for each subject (Fig. 4A, black disks). For example, for subject Co, the fit equation was (Becker 1991)
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A multiple regression analysis was performed to determine the parameters influencing catch-up saccade programming. The dependent variable was the amplitude (corrected horizontal amplitude SX* and corrected vertical amplitude SY*) and the independent variables were the position error taken 100 ms before the beginning of the saccade (PE100X and PE100Y) and the retinal slip taken at the same time (RS100X and RS100Y). These two signals had the best correlation coefficients with S*.
SINGLE-PEAKED SACCADES.
All correlation coefficients were significant (Table 2; Student's t-test, P < 0.01). The best first-order regression was obtained with PE100 as an independent variable. However, the correlation was even better for the second-order regression (Student's t-test, P < 0.01). Thus both variables were taken into account in the single-peaked saccadic programming
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; Eq. 1). Thus these results are fully compatible with a 2D extension of the results found in 1D. As in 1D (de Brouwer et al. 2002), the PE100 coefficient can be interpreted as a gain of compensation for PE and the RS100 coefficient as the time window of integration of velocity error (prediction of accumulation of velocity error).
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20% smaller in the second-order equation
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Figure 5 shows the different correlation coefficients of SX1* and SX2* with PE100X and RS100X (results are similar for the vertical component). It shows that the correlations between the two saccadic parts and the two signals are very different: PE100 was better correlated with SX1* (Fig. 5A), whereas RS100 was better correlated with SX2*(Fig. 5D). Thus PE100 and RS100 play a more important role in the programming of the first and the second part, respectively. Consequently, there is an asynchrony between PE and RS signals. PE was essentially taken into account in the first part, and then RS led to a reacceleration of the eye and to the second part of the double-peaked saccade. It corroborates what was previously observed in Fig. 3.
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). However, it is possible that the saccadic programming of the second part takes into account signals measured later than 100 ms before the beginning of the saccade. We performed multiple regression analyses with PE and RS measured 75, 50, and 25 ms before the beginning (PEt and RSt). We also tested a corrected PE signal (the saccadic amplitude already performed by the 1st part of the double-peaked saccade was removed from PE25). In all cases, the best correlation coefficient was obtained with the second-order regression (Student t-test, P < 0.01). Meanwhile, none of these regressions presented a significantly better fit than the regression performed with PE100 and RS100. In conclusion, statistical tests do not allow to conclude the precise instant at which signals are sampled for the second part of double-peaked saccade programming. Influence of saccade latency on saccade programming
The asynchrony hypothesis predicts that shorter latency saccades should show a smaller influence of RS than longer latency saccades. We specifically tested this prediction for single-peaked saccades and performed a multiple regression analysis after separating the data in four sets of identical size on the basis of saccade latency (quartiles I, II, III, and IV). In agreement with the prediction, we found a monotonic increase of the gain of RS in Eq. 2 (range: 0.072–0.086) and Eq. 3 (range: 0.066–0.094) across the four quartiles. The fact that saccade latency plays a prominent role in the relative contribution of RS in saccade programming is shown in Fig. 6. The partial correlation coefficient of RS (Fig. 6A) in saccade programming increases with saccade latency for both horizontal (X) and vertical (Y) components. In contrast, the partial correlation coefficient of PE (Fig. 6B) is not affected by saccade latency. Altogether, the results reported in Fig. 6 show that saccade latency has no clear influence on PE estimation, whereas RS estimation is significantly better for longer latency saccades. Thus on average, PE was estimated before RS. However, there seems to be a lot of variability in the time lag between PE and RS estimation. This is shown by the observation that saccade latency had no systematic influence on RS estimation. In some cases, RS was even better estimated for short-latency than long-latency saccades as is shown in Figs. 2 and 3 (better estimation and shorter latency in Fig. 2). Thus even though there is a clear trend for longer latency saccades to better take into account RS, this is not always the case, and there is no systematic time lag between PE and RS estimation.
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Figure 2 showed a saccade directed toward the extrapolated target position. This saccade was single-peaked and straight. In contrast, Fig. 7 shows a single-peaked saccade that was highly curved. The initial orientation of the saccade was almost parallel to PE vector (PE solid arrow in Fig. 7C), whereas the final orientation was almost parallel to RS vector (RS solid arrow). Thus the saccade was first oriented toward the target position 100 ms before saccade onset and gradually took the movement of the target into account to be finally oriented in the same direction as the retinal slip signal. The instantaneous direction of this single-peaked catch-up saccade revealed an asynchrony between PE and RS signals: RS was taken into account with some delay, as was the case for double-peaked saccades.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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2D catch-up saccade programming
Recently, de Brouwer et al. (2002, 2001) quantitatively studied horizontal catch-up saccades in cats and in humans. They showed that both PE and RS were correlated with catch-up saccade amplitude and proposed a model for catch-up saccades programming. However, the analysis of the role of PE and RS orientation in catch-up saccade curvature was not possible in 1D (de Brouwer et al. 2002). Thus the presentation of 2D stimuli was a key element in uncovering the asynchrony between PE and RS signals in this study. In 2D, Engel et al. (1999) reported an influence of prediction on saccade direction. Saccade direction was best predicted by the sum of PE and a signal proportional to target velocity, integrated during 30 ms on average. They proposed a separation of the processing of amplitude and direction because the saccade amplitude did not take into account the predictive component in their data. However, this was probably because of their experimental conditions. Indeed, first, the target velocity only varied between two values (15 or 30°/s). Second, only the direction of the target ramp changed and its vectorial velocity remained constant with no position step. In this study, we introduced a position step and a velocity step, randomized both in amplitude and orientation. The advantage of randomizing independently both position and velocity steps of the target is that it allowed to cover a much wider range of sensory parameters PE and RS and to assess their respective role in saccade programming independently. This is not possible when only a velocity step is introduced as in Engel et al. (1999). In that case, PE is only the consequence of accumulated RS, and both variables are strongly coupled. We showed that single-peaked catch-up saccade amplitude and direction were correlated with PE and RS. Thus we showed that both saccade direction and amplitude were influenced by prediction.
Saccades often present asymmetrical velocity profiles: the acceleration phase is shorter than the deceleration phase (Van Opstal and Van Gisbergen 1987). We observed this characteristic in 2D catch-up saccades. Moreover, we also observed a large number of saccades presenting not only asymmetrical but double-peaked velocity profiles: the deceleration was not over when a second acceleration occurred. The two parts of double-peaked catch-up saccades presented very different correlation coefficients with PE and RS: the first part was better correlated with PE, whereas the second part was better correlated with RS. Thus double-peaked saccades programming revealed an asynchrony between PE and RS signals. The first part of these saccades principally took the PE signal into account. This part very poorly compensated for the target motion. A second part based on RS signal was triggered to correct the accumulated error caused by a bad estimation of the relative target motion. This correction took place before the first saccade was over and led to a reacceleration in the vectorial velocity profile. A priori, the occurrence of double-peaked saccades could be explained by the shorter latency of these saccades. Indeed, a shorter latency would increase the probability that RS is not taken into account in saccade programming. This is compatible with our finding that, for single-peaked saccades, RS is significantly better taken into account for larger latency saccades. In our data, the latency of double-peaked saccades was significantly shorter than for single-peaked saccade (Table 1). However, this difference was very small (
12 ms) in comparison with the SD of saccade latency (40 ms) and is probably not the main parameter influencing the occurrence of double-peaked saccades.
Saccade curvature
Asymmetrical velocity profiles can be associated with saccades presenting a change in direction, which can be gradual to instantaneous. A small asynchrony between PE and RS signals could lead to single-peaked but highly curved saccades when these signals have very different orientations. This can be observed in the example of Fig. 7 for which the two signals are perpendicular: this single-peaked saccade was first oriented in the direction of PE and was characterized by a strong curvature in the direction of RS. Previous studies have reported the curvature of 2D saccades to stationary targets. The curvature was direction-dependent. Purely horizontal or vertical saccades were weakly curved, whereas oblique saccades had a maximal curvature (Smit and Van Gisbergen 1990). Moreover, the sign of the curvature value always indicated a lead of the horizontal component (Viviani et al. 1977). Our analysis of control trials confirmed all these results. Catch-up saccades presented the same direction-dependent curvature. However, our protocol showed an influence of the angle between PE and RS signal orientation on the magnitude of the curvature. Saccade curvature was not fundamentally determined by target motion but was modulated around curvature for controls.
Parallel processing
Previously, two types of experimental paradigms were used to show that the saccadic system can process visual information during saccade programming: double step experiments and visual search paradigms. Saccades resulting from these experiments presented trajectories similar to the saccades studied in our protocol. In the double step paradigm, the second step of the target occurs when the system is already preparing the saccade response to the first step. One saccade can be triggered or two saccades with a very short intersaccadic interval. Parallel processing is shown: as the second saccade latency can be very short, or even zero, the system must have planned the second saccade while the first was executed or prepared (Becker and Jürgens 1979). Among the different tasks with distractors used to study parallel saccade processing, McPeek et al. (2000) used visual distractors and obtained very short intersaccadic intervals (10–100 ms). The first saccade toward the distractors was often hypometric and could not be explained by simple averaging. They showed that these saccades were not interrupted in flight. Thus the second saccade must have been processed in parallel with the first one. Furthermore, in subsequent analyses in monkeys (McPeek and Keller 2001; McPeek et al. 2003), they also obtained highly curved saccades. They suggested that this curvature could be caused by the competition between two populations of neurons simultaneously encoding two different saccade goals on a common motor map. Indeed, superior colliculas (SC) activity in the period immediately preceding the onset of the saccade was determinant in saccadic curvature. However, all these studies, using double-step or distractors, only observed processing of retinal position error during initial saccade programming and execution. The direction change in the ongoing saccades compensated for a new PE. Their paradigms did not introduce any retinal slip before saccade onset or during saccade execution.
Neuronal pathways
Our results are compatible with the hypothesis that PE and RS signals are processed in different neuronal pathways. Indeed, Newsome et al. (1985) observed deficits in smooth and saccadic eye movements made to moving targets after middle temporal lesions in monkeys, while these lesions did not affect saccades to stationary targets. Later, Keller et al. (1996) showed that the superior colliculus was only involved in the encoding of PE for catch-up saccades during pursuit. This suggests that a parallel pathway that does not include the colliculus is responsible for the saccadic part based on target motion (Krauzlis 2004). However, these signals must converge before the final output pathway of the oculomotor system (Keller and Missal 2003). Potential sites in which the integration of these two signals could take place are the nucleus reticularis tegmenti pontis (NRTP) (Crandall and Keller 1985; Suzuki et al. 1999, 2003; Yamada et al. 1996) and the vermis in the cerebellum (Krauzlis and Miles 1998; Matsuzaki and Kyuhou 1997; Takagi et al. 1998, 2000). This is compatible with a recent model of the saccadic system where the cerebellum plays an important role in the saccadic control, receiving information from the colliculus and being responsible for the control of saccade trajectory (Lefèvre et al. 1998; Quaia et al. 1999).
Thus we hypothesize that there are two parallel pathways: a position pathway (SC) and a motion pathway [middle temporal cortex (MT), medial superior temporal cortex (MST)]. If the motion path needs more time to correctly integrate RS than the time needed by the position path to evaluate PE, the two signals could not be synchronized. Using our 2D double-step-ramp paradigm with particular parameters could facilitate the detection of two parallel pathways and their interaction in electrophysiological studies. The analysis of the timing of activation of different parts of the brain could be compared with saccade properties such as velocity peaks and saccadic curvature. Activations caused by retinal PE or velocity error will be distinguishable in the case of an asynchrony between theses signals. Suggested parameters to observe an asynchrony between PE and RS would be a large RS (RS > 20°/s) and a large difference between the orientation of PE and RS.
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FOOTNOTES |
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Address for reprint requests and other correspondence: P. Lefèvre, CESAME, Université Catholique de Louvain, 4, av. G. Lemaître, 1348 Louvain-la-Neuve, Belgium (E-mail: lefevre{at}csam.ucl.ac.be)
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REFERENCES |
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